1. Field of the Invention
This invention relates to improved techniques for simulation of fabric dynamics and more specifically to explicit time discretization techniques of the differential equations for cloth simulation.
2. Description of the Prior Art
Conventional animation has always been a labor intensive project. Having human effort create each and every image used to generate the animation allowed extensive control over how items to be animated appeared. The cost of the extensive control is paid in human labor. As more computers are used to generate animation, Human labor is minimized by using computer simulations to generate many of the frames embodying the animation.
Conventional computer simulation techniques for cloth and soft body animation are of two varieties, simple and complex. The complex techniques yield acceptable animation results but require large computational resources and may require several iterations to achieve the desired result. Simple techniques are computationally efficient and their results are crude and simple. Using simple simulation techniques may require many iterations to achieve a functional simulation from which marginal animation may be generated. What is needed is a computationally efficient simulation for cloth and soft body animation that yields realistic results.
In a first aspect, the present invention includes a new technique for time differencing the underlying differential equations involved in the simulation of fabric dynamics. This new formulation is based on the separation of the damping force terms which are derived from the relative grid velocities and the tensile and bending stiffness terms which are derived from the relative grid positions. The time integration strategy is based on the evaluation of the stiffness and damping terms to produce a new velocity state and this new velocity state is then used to update the grid geometry. This separation of terms allows the formulation of a system which displays dynamically neutral behavior for wave propagation phenomena and stable integration of the damping terms. This force separation approach results in a time integration scheme which is four times more efficient than the commonly used backwards Euler (sometimes referred to as 2nd order Runga-Kutta) scheme since it allows time steps to be twice as long with each time step having half the computational complexity. It is also twice as efficient as the leapfrog time differencing techniques which are subjects of current research without any of the mode-splitting and problems associated with leapfrog methods. When the simulation of high tensile stiffness fabrics is required the technique lends itself to the use of explicit sub-cycling where the tensile stiffness terms are integrated separately with a smaller and simpler time step than the bending and damping forces.
In another aspect, the present invention simulates motion of a flexible surface using the steps of representing the flexible surface with a polygonal mesh interconnecting a plurality of points and calculating a new position of each point of the polygonal mesh over time using a first order differential equation for position and calculating a new velocity of each point of the polygonal mesh over time using a first order differential equation for velocity.
In still another aspect, the present invention simulates motion of a flexible surface using the steps of representing the flexible surface with a polygonal mesh interconnecting a plurality of points, calculating each point""s position over time using a first order differential equation employing an old position and an old velocity to determine a new position and calculating each point""s velocity over time using a first order differential equation employing the new position and current velocity to determine the new velocity.
In a further aspect, the present invention simulates motion of a flexible surface using the steps of representing the flexible surface with a polygonal mesh interconnecting a plurality of points and calculating a new first characteristic and a new second characteristic of each point of the polygonal mesh over time using a first order differential equation for the first characteristic and a first order differential equation for the second characteristic.
These and other features and advantages of this invention will become further apparent from the detailed description and accompanying figures that follow. In the figures and description, numerals indicate the various features of the invention, like numerals referring to like features throughout both the drawings and the description.